(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
An implicit discontinuous Galerkin method is introduced to solve the time-domain Maxwell's equations in metamaterials. The Maxwell's equations in metamaterials are represented by integral-differential equations. Our scheme is based on discontinuous Galerkin method in spatial domain and Crank-Nicolson method in temporal domain. The fully discrete numerical scheme is proved to be unconditionally stable. When polynomial of degree at most p is used for spatial approximation, our scheme is verified to converge at a rate of O(τ^2+h^p+1/2). Numerical results in both 2D and 3D are provided to validate our theoretical prediction.